# Spaces of positive intermediate curvature metrics

@article{Frenck2021SpacesOP, title={Spaces of positive intermediate curvature metrics}, author={Georg Frenck and Jan-Bernhard Kordass}, journal={Geometriae Dedicata}, year={2021} }

In this paper we study spaces of Riemannian metrics with lower bounds on intermediate curvatures. We show that the spaces of metrics of positive p-curvature and k-positive Ricci curvature on a given high-dimensional $$\mathrm {Spin}$$
Spin
-manifold have many non-trivial homotopy groups provided that the manifold admits such a metric.

## One Citation

Positive (p,n)-intermediate scalar curvature and cobordism

- MathematicsJournal of Geometry and Physics
- 2022

## References

SHOWING 1-10 OF 45 REFERENCES

Homotopy groups of the moduli space of metrics of positive scalar curvature

- Mathematics
- 2010

We show by explicit examples that in many degrees in a stable range the homotopy groups of the moduli spaces of Riemannian metrics of positive scalar curvature on closed smooth manifolds can be…

Riemannian metrics of positive scalar curvature on compact manifolds with boundary

- Mathematics
- 1987

We prove that any metric of positive scalar curvature on a manifold X extends to the trace of any surgery in codim > 2 on X to a metric of positive scalar curvature which is product near the…

On the space of riemannian metrics satisfying surgery stable curvature conditions

- Mathematics
- 2018

We utilize a condition for algebraic curvature operators called surgery stability as suggested by the work of S. Hoelzel to investigate the space of riemannian metrics over closed manifolds…

ON THE HOMOTOPY TYPE OF THE SPACE R + (M)

- Mathematics
- 2004

In this paper it is shown that the space of metrics of positive scalar curvature on a manifold is, when nonempty, homotopy equivalent to a space of metrics of positive scalar curvature that restrict…

Stability of the p-Curvature Positivity under Surgeries and Manifolds with Positive Einstein Tensor

- Mathematics
- 1997

We establish the stability of the class of manifolds with positive p-curvature under surgeries in codimension ≥ p + 3. As a consequence of this result, we first obtain the classification of compact…

$H$-space structures on spaces of metrics of positive scalar curvature

- MathematicsTransactions of the American Mathematical Society
- 2021

We construct and study an $H$-space multiplication on $\mathcal R^+(M)$ for manifolds $M$ which are nullcobordant in their own tangential $2$-type. This is applied to give a rigidity criterion for…

The two definitions of the index difference

- Mathematics
- 2013

Given two metrics of positive scalar curvature metrics on a closed spin manifold, there is a secondary index invariant in real $K$-theory. There exist two definitions of this invariant, one of…

Cobordism invariance of the homotopy type of the space of positive scalar curvature metrics

- Mathematics
- 2011

This is the publisher’s final pdf. The published article is copyrighted by the American Mathematical Society and can be found at: http://www.ams.org/publications/journals/journalsframework/proc.

Infinite loop spaces and positive scalar curvature in the presence of a fundamental group

- MathematicsGeometry & Topology
- 2019

This is a continuation of our previous work with Botvinnik on the nontriviality of the secondary index invariant on spaces of metrics of positive scalar curvature, in which we take the fundamental…

THE COHOMOLOGY OF BSOn AND BOn WITH INTEGER COEFFICIENTS

- Mathematics
- 2010

The cohomology rings of BSOn and BOn, with integer coefficients, are given by generators and relations expressed in terms of characteristic classes. Recently I wished to know the cohomology, with…